The ``invisible functions table'' is an alist with elements of the following
form, where fn is a function symbol and the ufni are unary function
symbols in the current ACL2 world, and k is at least 1.

(fn ufn1 ufn2 ... ufnk)

This table thus associates with certain function symbols, e.g., fn
above, a set of unary functions, e.g., the ufni above. The ufni
associated with fn in the invisible functions table are said to be
``invisible with respect to fn.'' If fn is not the car of any
pair in the alist, then no function is invisible for it. Thus for
example, setting the invisible functions alist to nil completely
eliminates the consideration of invisibility.

The notion of invisibility is involved in the use of the
:loop-stopper field of :rewrite rules to prevent the indefinite
application of permutative rewrite rules. Roughly speaking, if
rewrite rules are being used to permute arg and (ufni arg) inside of
a nest of fn calls, and ufni is invisible with respect to fn, then
arg and (ufni arg) are considered to have the same ``weight'' and
will be permuted so as to end up as adjacent tips in the fn nest.
See loop-stopper.